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VNumber -- a package for computing the v-number and v-function

Description

VNumber is a package for computing the v-number of homogeneous ideals and v-function of monomial ideals

Authors

Version

This documentation describes version 1.0 of VNumber, released September 12, 2024.

Citation

If you have used this package in your research, please cite it as follows:

@misc{VNumberSource,
  title = {{VNumber: compute v-number of homogeneous ideals and v-function of monomial ideals. Version~1.0}},
  author = {Antonino Ficarra and Emanuele Sgroi},
  howpublished = {A \emph{Macaulay2} package available at
    \url{https://github.com/Macaulay2/M2/tree/stable/M2/Macaulay2/packages}}
}

Exports

  • Functions and commands
    • isStablePrime -- test whether a prime ideal is a stable prime of a ideal $I$
    • reesMap -- compute the Rees map of $I$
    • soc -- compute the $\text{Soc}_\mathfrak{p}^*(I)$, where $I$ is a monomial ideal
    • stableMax -- compute the set of stable primes of a monomial ideal that are maximal with respect to the inclusion.
    • stablePrimes -- compute the set of stable primes of a monomial ideal
    • vFunction -- compute the $\text{v}$-function of monomial ideal $I$
    • vFunctionP -- compute the $\text{v}_\mathfrak{p}$-function of monomial ideal $I$
    • vNumber -- compute the $\text{v}$-number of homogeneous ideal $I$
    • vNumberP -- compute the $\text{v}_\mathfrak{p}$-number of homogeneous ideal $I$
  • Methods
    • isStablePrime(Ideal,Ideal) -- see isStablePrime -- test whether a prime ideal is a stable prime of a ideal $I$
    • reesMap(Ideal) -- see reesMap -- compute the Rees map of $I$
    • soc(Ideal,Ideal) -- see soc -- compute the $\text{Soc}_\mathfrak{p}^*(I)$, where $I$ is a monomial ideal
    • stableMax(Ideal) -- see stableMax -- compute the set of stable primes of a monomial ideal that are maximal with respect to the inclusion.
    • stablePrimes(Ideal) -- see stablePrimes -- compute the set of stable primes of a monomial ideal
    • vFunction(Ideal) -- see vFunction -- compute the $\text{v}$-function of monomial ideal $I$
    • vFunctionP(Ideal,Ideal) -- see vFunctionP -- compute the $\text{v}_\mathfrak{p}$-function of monomial ideal $I$
    • vNumber(Ideal) -- see vNumber -- compute the $\text{v}$-number of homogeneous ideal $I$
    • vNumberP(Ideal,Ideal) -- see vNumberP -- compute the $\text{v}_\mathfrak{p}$-number of homogeneous ideal $I$
  • Symbols
    • control -- optional argument for vFunctionP and vFunction

For the programmer

The object VNumber is a package, defined in VNumber.m2.


The source of this document is in /build/reproducible-path/macaulay2-1.25.06+ds/M2/Macaulay2/packages/VNumber.m2:547:0.